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# 4e4 math

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I am currently working on the basic math behind the 4e4 entry gameplay.

There are basically two checks that will be used whenever you need to do something. They are:

- The linear check, which compares the value of an attempt (useful abilities and bonuses) against a difficulty (based on defensive abilities of the target and bonuses). Basically, if you have an attempt of A and a difficulty of D, the probability of success is (A - D + 50) %

(A-D) P(w)
< -50 0%
-40 10%
-25 25%
-10 40%
0 50%
10 60%
25 75%
40 90%
> 50 100%

- The luck check acts as a short-circuit in several situations. It is based on the hidden luck ability of the player, which can be increased by some items and spells. The initial luck stat is 0, it can increase up to 100. The test is, in fact, a series of Bernouilli attempts of success probability 0.01, one success is enough to pass the check. Therefore, the success table is:

LUCK P(l)
0 0%
1 1%
2 2%
3 3%
4 4%
5 5%
6 6%
7 7%
8 8%
9 9%
10 9%
20 18%
30 26%
40 33%
50 39%

I am however thinking of changing the estimation method at 50, for instance by making it linear, and a success probability of (Luck-11)% : total chance of luck shortcut 89% at Luck 100.

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